Non-Fermi-liquid regime of a doped Mott insulator

We study the doping of a Mott insulator in the presence of quenched frustrating disorder in the magnitude and sign of the magnetic exchange. Two quite different doping regimes δ<δ* and δ>δ* are found, with δ*J/t (J is the characteristic magnitude of the exchange, and t the hopping amplitude). In the high-doping regime, a (Brinkman-Rice) Fermi-liquid description applies with a coherence scale of order δt. In the low-doping regime, local magnetic correlations strongly affect the formation of quasiparticles, resulting in a very low coherence scale εF*J(δ/δ*)². Fermi-liquid behavior does apply below εF*, but a ``quantum-critical regime'' εF*<T<J holds, in which marginal Fermi-liquid behavior of several physical properties is found: NMR relaxation time 1/T₁~const, resistivity ρdc(T)∝T, optical lifetime τₒₚₜ^-1∝ω/ln(ω/εF*) together with ω/T scaling of response functions, e.g., $J{{∑}}_{{{→}}{q}}{{χ}}^{{''}}({{→}}{q},{ω}){∝}tanh({ω}/2T).$ In contrast, single-electron properties display stronger deviations from Fermi-liquid theory in this regime with a $√{{ω}}$ dependence of the inverse single-particle lifetime and a $1/√{{ω}}$ decay of the photoemission intensity. On the basis of this model and of various experimental results, it is argued that the proximity of a quantum-critical point separating a glassy Mott-Anderson insulator from a metallic ground state is an important ingredient in the physics of the normal state of cuprate superconductors. In this picture the corresponding quantum critical regime is a spin liquid with incoherent holes and a slow state of spins and holes with slow spin and charge dynamics responsible for the anomalous properties of the normal state. This picture may be particularly relevant to Zn-doped materials.